Question on range of function

Given f(x) = 1/(x-1) and g(x)= x^2 -1 and h(x) = sqrt(2x+4)

what is the range of f(x)*g(x)

I put that it's all reals and that's wrong.

also the range for g(x)/f(x)

Since this is a rational function with an oblique asymptote I put all reals but that's also wrong

and finally the domain and range for h(h(x))?

After solving the equation 2(sqrt(2x+4)+4 >= 0 I got x>= 0. I put that for the domain and apparently it's wrong. also for the range I put y>=4 and that came out wrong too

Why am i doing these wrong? am i missing something?

Re: Question on range of function

Hey mikewezyk.

Hint: For the first one find the limit as x->1 f(x)*g(x) and then factorize f(x)*g(x) when x != 1 (remember (a+b)(a-b) = a^2 - b^2).